Physics: Momentum Problem

Hello!

I need your guys help for this momentum problem... I have really no idea.


Question:

An 80 kg astronaut (body mass only) drifting in space is 200 m away from her space shuttle, and moving along with it (i.e. she is stationary with respect to the shuttle). Her thruster pack is damaged, and she only has 4 minutes of air left. If she unstraps her 10 kg tool kit and throws it away at a speed of 8 m/s, can she make it back to the shuttle? More importantly, will she still be breathing?


Answer: 240 s available needs, 200 s

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I have physics final exam on next week, I really need to know the steps and clear equations.


Thank you so much! I would really really appreciate that! ^___^

To find her approach velocity Va, use conservation of momentum:

Mt*Vt = Ma*Va or
Va = Mt*Vt/Ma = 10*8/80 = 1 m/s

Time to reach shuttle t = D/Va = 200/1 = 200 sec

Since 200 sec is less than 240 sec (4 min), she will still be breathing.

Since you specifically stated that her body mass (only) is 80 kg, it is incorrect to subtract the kit mass from that value. Also, (10)(8)/(80 - 10) = 1.14 m/s, not .875..........

You do know that the shuttle can backup to retrieve her.. The weight on her tool belt has no effect on time and space as everything no matter what the mass is has the same speed everything around her.. Only a forward or backwards push can get you lost about and around the shuttle.. Other that that.. You are moving the same speed as the shuttle... Just do not push yourself away.. Then you will get lost...

conservation of momentum

P(astronaut) = P(toolkit)

mv = mv

(80-10)v = (10)(8)
v = .875 m/s
200/.875 = 228s
4(60) = 240s

228s < 240s

yes the astronaut will make it.